Two cell phone companies have different rate plans. Runfast has monthly charges $8 plus $8 per gig of
data. B A &D’s monthly charge is $15 plus $4 per gig of data. Your task is to determine under what
circumstances each company has the better pricing. You will derive and solve a set of equations, graph
those equations, and evaluate the meanings for these events. Don’t worry; I have a series of questions
to guide you through the process. Good luck!
1. Determine the equation for the monthly charges for Runfast and BA&D. (2 points)
Runfast= ______________________
BA&D=________________________
2. Use your mathematical skill to solve this system of equations using the substitution method. (4
points)
Show your work here:

ANSWER

C. 35 men

EXPLANATION

Let m represent the number of men needed and d represent the number of days.

From the question,the number of men needed varies inversely to the time needed to complete the project.

We can write the inverse variation equation.

[tex]m = \frac{k}{d} [/tex]

where k is the constant of variation.

When m=28, d =90.

We substitute these values into the variation equation to determine the value of k.

[tex]28 = \frac{k}{90} [/tex]

[tex]k = 90 \times 28[/tex]

[tex]k = 252[/tex]

Now the equation becomes:

[tex]m= \frac{2520}{d} [/tex]

When d=72,

[tex]m = \frac{2520}{72} [/tex]

[tex]m = 35[/tex]

Therefore he needs to have 35 men working.

A horizontal shift happens when you add or subtract a value from the input value of x.

To shift left the number would be added to the x.

The answers are:

h(x) = 3 ln(x + 3) + 1

r(x) = −3 ln(x + 1) + 3

p(x) = ln(x + 2) − 2

Answer:

h(x) = 3 ln(x + 3) + 1

r(x) = −3 ln(x + 1) + 3

p(x) = ln(x + 2) − 2

Step-by-step explanation:

The parent function given to us is: [tex]f(x)=\ln x[/tex].

A horizontal translation to the left k units is of the form [tex]y=\ln (x+k)[/tex].

This implies that;

h(x) = 3 ln(x + 3) + 1, is a horizontal translation to the left by 3 units.

r(x) = −3 ln(x + 1) + 3, is a horizontal translation to the left by 1 unit.

p(x) = ln(x + 2) − 2, is a horizontal translation to the left by 2 unit.

Answer:

The answer should be D. It is -2 on the inside because it is backwards of what you may think and because it is inside the square root. The -3 represents a down shift of 3

Answer: Last option.

Step-by-step explanation:

Below are shown some transformation for a function f(x):

[tex]f(x) + k[/tex] shifts the function k units upward.

[tex]f(x) - k[/tex] shifts the function k units downward.

[tex]f(x+k)[/tex] shifts the function k units to the left.

[tex]f(x-k)[/tex] shifts the function k units to the right.

Then, knowing that the graph of the function [tex]y=\sqrt{x}[/tex] is shifted 3 units down and 2 units rights, the function that represents the new graph is:

[tex]y=\sqrt{x-2}-3[/tex]

Which is the last option.

the only equation that seems to describe the pattern is:

[tex]\( b = a - 5 \)[/tex]. Therefore, option C is correct

To determine whether the given equations can describe the pattern in the table, we need to look at the values in the table and see if they satisfy the equations. However, the provided image is not completely clear, and it seems like part of the table or the values might be missing.

From what is visible in the image, it seems we have a table with two columns labeled 'a' and 'b', with 'a' taking on values from 5 to 9 and 'b' from 0 to 4. We need to check if the equations given describe the relationship between 'a' and 'b' according to the table.

The equations given are:

1. [tex]\( b + a = 5 \)[/tex]

2. [tex]\( b = a + 5 \)[/tex]

3. [tex]\( b = a - 5 \)[/tex]

4. [tex]\( a = b - 5 \)[/tex]

Without the complete table, we can't perform a full analysis, but we can explain how you would generally approach this:

- For equation 1 [tex](\( b + a = 5 \))[/tex], check if the sum of each pair of 'a' and 'b' equals 5.

- For equation 2 [tex](\( b = a + 5 \))[/tex], check if 'b' is always 5 more than 'a'.

- For equation 3 [tex](\( b = a - 5 \))[/tex], check if 'b' is always 'a' minus 5.

- For equation 4 [tex](\( a = b - 5 \))[/tex], check if 'a' is always 'b' minus 5.

Given the values for 'a' and 'b' in the table:

a | 5 | 6 | 7 | 8 | 9

b | 0 | 1 | 2 | 3 | 4

We can analyze each equation to see if it describes the pattern in the table.

1. [tex]\( b + a = 5 \)[/tex]

Let's check if the sum of 'a' and 'b' equals 5 for each pair:

- For [tex]\( a = 5 \), \( b = 0 \): \( 5 + 0 = 5 \)[/tex] (True)

- For [tex]\( a = 6 \), \( b = 1 \): \( 6 + 1 = 7 \)[/tex] (False)

- Since it is false for [tex]\( a = 6 \), \( b = 1 \)[/tex], we can already conclude that this equation does not describe the pattern.

2. [tex]\( b = a + 5 \)[/tex]

Let's check if 'b' equals 'a' plus 5:

- For [tex]\( a = 5 \), \( b = 0 \): \( 5 + 5 = 10 \)[/tex] (False)

- Since it is false for [tex]\( a = 5 \), \( b = 0 \)[/tex], this equation does not describe the pattern.

3. [tex]\( b = a - 5 \)[/tex]

Let's check if 'b' equals 'a' minus 5:

- For [tex]\( a = 5 \), \( b = 0 \): \( 5 - 5 = 0 \)[/tex] (True)

- For [tex]\( a = 6 \), \( b = 1 \): \( 6 - 5 = 1 \)[/tex] (True)

- Continuing this pattern, this equation seems to be true for all given pairs of 'a' and 'b'.

4. [tex]\( a = b - 5 \)[/tex]

This is not likely to be true since subtracting 5 from 'b' would result in negative numbers, which are not present in the 'a' values.

From the analysis, the only equation that seems to describe the pattern is:

[tex]\( b = a - 5 \)[/tex]

Let's confirm that this equation is true for all pairs of 'a' and 'b'.

The equation [tex]\( b = a - 5 \)[/tex] holds true for all pairs of 'a' and 'b' values in the table. Therefore, this equation correctly describes the pattern in the table.

Answer:

Inscribed angle

Step-by-step explanation:

Answer

if your looking for an answer try to be smart and actually show a picture I cant do nothing with just a name thats how we us experts find answers pictures.

Step-by-step explanation:

Answer:

first things first which one is angle B. if would be easier if you labeled them .

Step-by-step explanation:

but any ways see if the image attached can help out

Answer:

b

Step-by-step explanation:

Divide the new price by 1 + percent of increase:

325 / 1.30 = 250

The original price was £250

Answer:

+- 5 and +- 3

Step-by-step explanation:

qn 2:

4r² = 91 + 9

4r² = 100

r² = 25

r = +- 5

qn 3:

4r² = 29 + 7

4r² = 36

r² = 9

r = +- 3

Answer:

Step-by-step explanation:

[tex]\bold{Q2.}\\\\4r^2-9=91\qquad\text{add 9 to both sides}\\\\4r^2-9+9=91+9\\\\4r^2=100\qquad\text{divide both sides by 4}\\\\\dfrac{4r^2}{4}=\dfrac{100}{4}\\\\r^2=25\to r=\pm\sqrt{25}\\\\\boxed{r=\pm5}[/tex]

[tex]\bold{Q3.}\\\\4r^2-7=29\qquad\text{add 7 to both sides}\\\\4r^2-7+7=29+7\\\\4r^2=36\qquad\text{divide both sides by 4}\\\\\dfrac{4r^2}{4}=\dfrac{36}{4}\\\\r^2=9\to r=\pm\sqrt9\\\\\boxed{r=\pm3}[/tex]

Answer:

I think its D

Step-by-step explanation:

Forgive me if im wrong.

Answer:

  1500(1.0115)^(2t)

Step-by-step explanation:

The formula for the balance in an account earning compound interest is ...

  A = P(1 +r/n)^(nt)

where P is the principal invested, r is the annual rate, n is the number of times per year interest is compounded, and t is the number of years.

__

Using the given values in the formula, we have ...

  A = 1500(1 +0.023/2)^(2t)

Simplifying a bit, this is ...

  A = 1500(1.0115)^(2t) . . . . . CD value after t years

Answer 1.37, 1 1/4, 1.16, 1 1/10

Step-by-step explanation:

1.37

1 1/4 (1.25)

1.16

1 1/10 (1.1)

Hello There!

-Ordered From Least To Greatest-

1 1/10 - 1.16 - 1 1/4 - 1.37

the correct answer would be 16 you add (2+2) first and the do 8/2 then multiple 4 x 4 and you get 16

[tex]\bf 8\div 2(2+2)\implies 8\div 2(\stackrel{\downarrow }{4})\implies \stackrel{\downarrow }{4}(4)\implies 16[/tex]

recall PEMDAS

Parentheses first off

MD multiplication and division from left-to-right.

Your answer is 5! (:

Answer:

5

Step-by-step explanation:

A square root of a number n is a number r such that r2=n. in the case 25 we find that 52=25 , so 5 is a square root of 25. sorry if this is confusing. found this from google.

The top right graph has a slope of 1/3

Answer:

top right

Step-by-step explanation:

Answer:

The number of messages sent by Justin was [tex]180\ messages[/tex]

The number of messages sent by David was [tex]270\ messages[/tex]

Step-by-step explanation:

Let

x-----> number of messages sent by Justin

y----> number of messages sent by David

we know that

[tex]\frac{x}{y}=\frac{8}{12}[/tex]

[tex]x=\frac{8}{12}y[/tex] ----> equation A

[tex]x+y=450[/tex] -----> equation B

substitute equation A in equation B and solve for y

[tex]\frac{8}{12}y+y=450[/tex]

[tex]\frac{20}{12}y=450[/tex]

[tex]y=450*12/20=270\ messages[/tex]

Find the value of x

[tex]x=\frac{8}{12}(270)=180\ messages[/tex]

therefore

The number of messages sent by Justin was [tex]180\ messages[/tex]

The number of messages sent by David was [tex]270\ messages[/tex]

The expression 5x + 5 ( x-3y ) + 1/2 (4x - 6y) simplifies to 12x - 18y by distributing the multiplication over addition, combining like terms, and checking the answer for reasonableness.

To simplify the algebraic expression 5x + 5 ( x-3y ) + ½ (4x - 6y), let's start by distributing the multiplication over addition for each term inside the parentheses:

Multiply 5 by each term inside the first set of parentheses: 5 × x and 5 × (-3y), which gives us 5x - 15y.

Multiply ½ by each term inside the second set of parentheses: ½ × 4x and ½ × (-6y), resulting in 2x - 3y.

Now, combine the like terms:

The x-terms: 5x + 5x + 2x = 12x.

The y-terms: -15y - 3y = -18y.

So, the expression in standard form is 12x - 18y.

Lastly, we should check the answer to see if it is reasonable:

No like terms are left to combine.

The coefficients are summed up correctly.

The expression is simplified as much as possible.

Answer:

x = ±10

Step-by-step explanation:

x^2 = 100

Take the square root of each side

sqrt(x^2) = sqrt(100)

x = ±10

[tex] 3 \ln 3 - \ln 9 = 3 \ln 3 - \ln 3 ^2 = 3 \ln 3 - 2 \ln 3 = \ln 3[/tex]

Answer: [tex]\ln 3[/tex]

Answer:

ln 3

Step-by-step explanation:

Using the rules of logarithms

• log [tex]x^{n}[/tex] ⇔ n logx

• log x - log y = log ([tex]\frac{x}{y}[/tex] )

Given

3 ln3 - ln9, then

= ln 3³ - ln 9

= ln 27 - ln 9

= ln ([tex]\frac{27}{9}[/tex] ) = ln 3

Answer:

The sequence 3 , 4 , 6 , 10 , 18 described by the 2nd term is t2 = 4 and recursive definition is tn+1 = 2 tn - 2 ⇒ 4th answer

Step-by-step explanation:

* Lets revise the recursive formula

1. Determine if the sequence is arithmetic (Do you add, or subtract, the

  same amount from one term to the next?)

2. Find the common difference. (The number you add or subtract.)

3. Create a recursive formula by stating the first term, and then stating

   the formula to be the previous term plus the common difference.

   a1 = first term;

   an+1= an + d

- Where:

# a1 = the first term in the sequence

# an = the nth term in the sequence  

# an+1 = the term after the nth term  

# n = the term number

# d = the common difference.

* Now lets solve the problem

∵ The recursive definition is tn+1 = 2 tn - 2 and t2 = 4

- Look to the answer we have three answer with second term = 4,

 1st , 2nd and 4th

- Lets find the 1st term

∵ t2 = 2 t1 - 2

∵ t2 = 4

∴ 4 = 2 t1 - 2 ⇒ add 2 to the both sides

∴ 6 = 2 t1 ⇒ divide the two sides by 2

∴ t1 = 3

- We have two answer with first term = 3, 2nd and 4th answers

* Lets find the third term

∵ t3 = 2 t2 - 2

∵ t2 = 4

∴ t3 = 2 (4) - 2 = 8 - 2 = 6

∴ The 4th answer has the third term = 6

* The 4th sequence 3 , 4 , 6 , 10 , 18 described by the 2nd term is

 t2 = 4 and recursive definition is tn+1 = 2 tn - 2

Answer:

Always.

Step-by-step explanation:

I can think of no example that makes always false.

Replacing the minimum value in a dataset with a smaller number can sometimes change the mean. Hence, the correct answer is B.

Sometimes, replacing only the minimum value in a dataset with a smaller number may change the mean.

For example, if the dataset is {1, 3, 4, 5} and you replace the minimum value 1 with 0, the mean changes from 3.25 to 3.

The complete question is given below.

If angle g measures 117º, what is the measure of supplementary angle h?

Angle g and angle h are the Supplementary angles. Then the measure of the angle ∠h  will be 63°.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

If angle g measures 117º.

Then the measure of angle h will be

We know that angle g and angle h are the Supplementary angles. Then we have

∠g + ∠h = 180°

117° + ∠h = 180°

         ∠h = 63°

More about the angled link is given below.

https://brainly.com/question/15767203

#SPJ2

Answer:

It's the first option.

Step-by-step explanation:

(x + 2)^2 gives a duplicate (multiplicity 2) root. (because (x + 2)^2 = 0 so x = -2 multplicity 2)

(x - 4) gives one root of 4.

(x + 1)^3  gives x = -1 with multiplicity 3.

Answer:

-2 with multiplicity 2, 4 with multiplicity 1, and -1 with multiplicity 3.

Step-by-step explanation:

The given polynomial function is: [tex]f(x)=(x+2)^2(x-4)(x+1)^3[/tex].

To find the roots of this polynomial, we equate each factor to zero.

This implies that;

i. [tex](x+2)^2=0[/tex], [tex]\implies x=-2[/tex], the multiplicity of this root is 2, because the factor repeats twice

ii.  [tex]x-4=0[/tex], [tex]\implies x=4[/tex], the multiplicity of this root is 1, because the factor repeats once.

ii.  [tex](x+1)^3=0[/tex], [tex]\implies x=-1[/tex], the multiplicity of this root is 3, because the factor repeats three times.

Answer:

I would say A, binocular vision. ((Not sure though.))

Step-by-step explanation:

Process of elimination. Opposable thumbs could help, but not as much as being able to spot your prey from far away. And what does singular births and just being a mammal help with being a predator? The answer that makes most sense is A. Hope this helps.

Answer:

I believe binocular vision or opposable thumbs

Step-by-step explanation:

Probably opposable thumbs because it helps predators grab things

The angels are ADJACENT ANGELS

Answer:

21

(Side Note: I solved this for anyone who needs the answer.)

Definitions:

Adjacent: Congruent meaning same measure.

Vertical: Two angles that have a common side.

Explanation:

This equation is adjacent.

If we look at this problem and look to the bottom and see that tiny square, that means it is a right angle, right angles equal to 90 degrees.

Step-By-Step:

To solve for x, we need to put 25 degrees and x into a formula.

x + 35 = 90

Next and the last step is to subtract 90 and 35:

90 - 35 = 21

Our final answer is 21.

            Hope this helps!

      ~Hocus Pocus

Step-by-step explanation:

To find the y-coordinate points we need to evaluate the function for all the [tex]x[/tex] values in the table. In other words, we need to replace [tex]x[/tex] with each value in our given function and simplify.

- For x = 0

[tex]f(x)=(x-2)^2-5[/tex]

[tex]f(0)=(0-2)^2-5[/tex]

[tex]f(0)=(-2)^2-5[/tex]

[tex]f(0)=4-5[/tex]

[tex]f(x)=-1[/tex]

Since [tex]x=0[/tex] and [tex]y=-1[/tex], our first point is (0, -1)

- For x = 1

[tex]f(x)=(x-2)^2-5[/tex]

[tex]f(1)=(1-2)^2-5[/tex]

[tex]f(1)=(-1)^2-5[/tex]

[tex]f(1)=1-5[/tex]

[tex]f(x)=-4[/tex]

Our second point is (1, -4)

- For x = 2

[tex]f(x)=(x-2)^2-5[/tex]

[tex]f(2)=(2-2)^2-5[/tex]

[tex]f(2)=(0)^2-5[/tex]

[tex]f(x)=-5[/tex]

Our third point is (2, -5)

- For x = 3

[tex]f(x)=(x-2)^2-5[/tex]

[tex]f(3)=(3-2)^2-5[/tex]

[tex]f(3)=(1)^2-5[/tex]

[tex]f(3)=1-5[/tex]

[tex]f(x)=-4[/tex]

Our fourth point is (3, -4)

- For x = 4

[tex]f(x)=(x-2)^2-5[/tex]

[tex]f(4)=(4-2)^2-5[/tex]

[tex]f(4)=(2)^2-5[/tex]

[tex]f(4)=4-5[/tex]

[tex]f(x)=-1[/tex]

Our fifth point is (4, -1)

Now we just need to plot each point in our coordinate plane and join them with the parabola as you can see in the attached picture.

17 and -17. The opposite of a number is usually the negative or positive version of that #

Answer: B

Step-by-step explanation:

There are 4 quarts in a gallon. 12 / 4 = 3.

A contains 3 gallons. B contains 2 gallons. If you divide the price by the number of gallons, b will be cheaper.

Answer:

B.

Step-by-step explanation:

A quart is approximately 1/4 of a gallon. Therefore 8 quarts is 2 gallons. 8/12 is 2/3

2/3 of $44.04 is $29.36. Therefore A is more expensive and B is the better buy.

Answer:

Probability the first is a communications major and the second is a business major = 0.03

Step-by-step explanation:

let the total number of students be 100

Event A= Business Majors = 15%

Event B = Communication Majors = 20%

P(A) = [tex]\frac{15}{100}[/tex]   ⇒  P(A) = 0.15

P(B) = [tex]\frac{20}{100}[/tex]  ⇒ P(B) = 0.2

P( A and B) = P(A) × P(B)

                  = 0.15 × 0.2

                  = 0.03                      

Answer:

3*3*3=27

The answer is B 1 1/27

Step-by-step explanation:

As a formula:  

volume = s3  

where:

s  is the length of any edge of the cube.

Read as "s to the power 3"